To manufacture an automobile requires​ painting, drying, and polishing. Epsilon Motor Company produces three types of​ cars, the​ Delta, the​ Beta, and the Sigma. Each Delta requires 7 hours for​ painting, 2 hours for​ drying, and 5 hours for polishing. A Beta requires 13 hours for​ painting, 4 hours for​ drying, and 6 hours for​ polishing, and a Sigma requires 5 hours for​ painting, 5 hours for​ drying, and 5 hours for polishing. If the company has 172 hours for​ painting, 97 hours for​ drying, and 125 hours for polishing per​ month, how many of each type of car are​ produced? Select the correct choice below and fill in any answer boxes within your choice.
A.
The Epsilon Motor Company produces nothing ​Deltas, nothing ​Betas, and nothing Sigmas in a month.
​(Simplify your​ answers.)
B.
There are infinitely many combinations of each type of car that can be produced. Using ordered​ triplets, the solution can be written as​ {(D, B,S) ​| D=nothing​, B=nothing​, S any real ​number}.
​(Simplify your answers. Type expressions using S as the variable as​ needed.)
C.
There is no possible combination of each type of car that can be produced that meets the criteria.